Silvestre began his career with Argentine club Boca Juniors, where he would go on to make his league debut on 23 March 2003 in a 3–1 win over Lanús.

[2] His first six months at Catania was not so great as he was not part of then-coach Silvio Baldini's starting team, making just 11 appearances, just five as a starter.

However, his loan was nonetheless made permanent in the summer of 2008 for €2.043 million[3] after Walter Zenga was appointed head coach, following the sacking of Baldini.

He formed a solid defensive line-up with the likes of Pablo Álvarez, Nicolás Spolli, Christian Terlizzi and Ciro Capuano as Catania recorded their record-breaking points total in Serie A, finishing in 13th place with just 45 goals conceded in 38 matches.

Silvestre made his Nerazzurri debut in the third qualifying round of the 2012–13 UEFA Europa League against Hajduk Split, a 3–0 away win.

[8][9] On 28 April 2013, in Inter's 1–0 defeat to Palermo, Silvestre incurred an injury to his right thigh, prematurely ending his season, making 20 total appearances.

He made his Rossoneri debut on 19 October in the 1–0 home victory against Udinese, and in the next round, a 3–2 defeat away to Parma, he scored his first goal with Milan.